To characterize the nature of the transformed data in the uniform probability space, it is convenient to introduce the concept of copula, a tool to analyze data dependence and construct multivariate distributions. Let \((U_1,U_2,\dots ,U_d)\)  be uniform random variables, then their joint cdf \(F_{U}(\mathbf {u}) = P(U_1\le u_1, \dots , U_d \le u_d)\)  is a copula \(C:[0,1]^d \rightarrow [0,1]\)  (see [1]}). The core of copulas resides in Sklar's theorem [2]} which states that if \(F_{X}\)  is a \(d\) -dimensional cdf with continuous marginals \(F_{X_1},\dots ,F_{X_d}\) , then \(F_{X}\)  has a unique copula representation
\(F_{X}(x_1,\dots ,x_d) = C_{U}(F_{X_1}(x_1),\dots ,F_{X_d}(x_d)).\) 
